A RESUME  OF  THE  VARIOUS  METHODS  EMPLOYED  FOR 
THE  DETERMINATION  OF  e/m  FOR  THE  ELECTRON 

BY 


CHARNJIT  SINGH 

B.  S.,  in  Electrical  Engineering,  University  of  Illinois, 

1917 


THESIS 


Submitted  in  Partial  Fulfillment  of  the  Requirements  for  the 


Degree  of 


MASTER  OF  SCIENCE 
IN  PHYSICS 


IN 


THE  GRADUATE  SCHOOL 

OF  THE 

UNIVERSITY  OF  ILLINOIS 


1921 


...  ■ ' ■ w 


\3£\ 
%k  G 


UNIVERSITY  OF  ILLINOIS 


THE  GRADUATE  SCHOOL 


May_az 19121 

I HEREBY  RECOMMEND  THAT  THE  THESIS  PREPARED  UNDER  MY 

SUPERVISION  BY. ChARNJ IT  SINGH 

ENTITLED A,MStIMiLPF_..m  EMPLOYED  FOR  ini?, 

DETERMINATION  OF  e/m  FOR  TiiE  ELECTRON 

BE  ACCEPTED  AS  FULFILLING  THIS  PART  OF  THE  REQUIREMENTS  FOR 


Recommendation  concurred  in* 

Committee 

on 

Final  Examination* 


*Required  for  doctor’s  degree  but  not  for  master’s 


A 


4 


Digitized  by  the  Internet  Archive 
in  2015 


https://archive.org/details/resumeofvariousmOOsing 


TABLE  OF  CONTENTS 


I HISTORICAL  SKETCH 1 

II  DETERMINATION  OF  e/m  

General  Theory 3 

Wiechert  Method 6 

Kaufman  Method.  9 

Thomson  Methods  

(a)  First  Method 13 

(b)  Second  Method 18 

III  DETERMINATION  OF  e/m  FOR  PARTICLES  SET  FREE  BY  ULTRA- 

VIOLET LIGHT  AND  FOR  THE  NEGATIVELY  CHARGED  PARTICLES 
EMITTED  BY  INCANDESCENT  SOLIDS  23 

(a)  Lenard's  Method 

(b)  Sir  J.J.  Thomson's  Method 25 

IV  M.  AND  MADAME  CURIE'S  INVESTIGATIONS  CONCERNING  RADIO- 
ACTIVE SUBSTANCES 

V SUMMARY  OF  RESULTS 

VI  CONCLUSION 33 

$ 


I.  HISTORICAL  SKETCH 

The  word,  "electron"  was  first  suggested  in  1891  by  Dr.  G. 
Johnson  Stoney  as  a name  for  the  natural  unit  of  electricity:  namely, 
that  quantity  of  electricity  wnicn  must  pass  through  a solution  in 
order  to  liberate  at  one  of  the  electrodes  one  atom  of  hydrogen  cr 
one  atom  of  any  equivalent  substance.  The  word  "electron"  was  intro- 
duced to  denote  simply  a definite  elementary  quantity  of  electricity 
without  any  reference  to  the  mass  or  inertia  which  may  be  associated 
with  it.  Professor  Stoney  implies  tnat  every  atom  must  contain  at 
least  two  electrons;  one  positive  and  one  negative,  because  other- 
wise, it  would  be  impossible  that  the  atom  as  a whole  be  electrically 
neut ral. 

It  is  obvious  that  a word  is  needed  which  denotes  merely  the 
elementary  unit  of  electricity  and  has  no  implications  as  to  where 
that  unit  is  found,  to  wnat  it  is  attached,  with  wnat  inertia  it  is 
associated,  or  whether  it  is  positive  or  negative  in  sign;  ana  it  is 
also  apparent  that  the  word  "electron"  is  the  logical  one  to  associ- 
ate with  this  conception.  J.J.  Thomson’s  word  corpuscle  is  a very 
appropriate  one  to  denote  tne  very  minute  inertia  with  which  the  nega 
tive  electron  is  found  associated  in  cathode  rays. 

With  the  discovery,  due  to  use  of  the  new  agency,  X rays, 
the  atom  as  an  ultimate  indivisible  rhing  was  gone,  and  tne  era  of 
the  constituency  of  the  atom  began.  And  witn  the  astonishing  rapid- 
ity during  the  past  twenty  five  years  the  properties  of  the  sub- 
atomic world  has  been  revealed. 

Physicists  began  at  once  to  ask  diligently  and  to  find  at 
least  partial  answers  to  questions  like  these: 

1.  What  are  the  masses  of  the  constituents  of  the  atoms  torn 


■ 


' 


. 


■ 


2 


asunder  by  x rays  ana  similar  agencies? 

2.  What  are  tne  values  of  the  charges  carried  by  tnese  con- 
st ituents? 

3.  How  many  of  these  constituents  are  there? 

4.  How  large  are  they,  i.e.,  what  volume  do  they  occupy? 

5.  What  are  their  relations  to  the  emission  and  absorption  of 
light  and  heat  waves,  i.e.,  of  electromagnetic  radiation? 

6.  Do  all  atoms  possess  similar  constituents?  In  other  words, 
is  there  a premordial  sub-atom  out  of  which  atoms  are  made? 

The  partial  answer  to  the  first  of  these  questions  came 
with  the  study  of  the  electrical  behavior  of  rarefied  gases  in  so- 
called  vacuum  tubes.  Sir  J.J.  Thomson  and  Wiechert  showed  independ- 
ently in  1897  that  the  value  of  e/m  for  the  negative  ion  in  sucn  ex- 

7 

hausted  tubes  is  about  1.8  x 10  electromagnetic  units,  or, about  180C 
times  the  value  of  e//m  for  hydrogen  ion  in  solution.  Since  the  ap- 
proximate equality  of  ne,  (n  is  the  number  of  molecules  per  cu.cm.) 
in  gases  and  solution  meant  that  e was  at  least  of  the  same  order  in 
both,  the  only  possible  conclusion  was  that  the  negative  ion  which 
appears  in  discharges  in  exhausted  tubes  has  a mass,  i.e.,  a»  inertia 
only  l/1800th  of  the  mass  of  the  lightest  known  atom,  namely,  the 
atom  of  hydrogen. 

Furthermore,  these  and  other  experiments  have  snown  that 
e/m  for  the  negative  carrier  is  always  the  same  wnatever  be  the  na- 
ture of  the  residual  gas  in  the  discharge  tube.  This  was  an  indi- 
cation of  an  affirmative  answer  to  the  sixth  question  above,  an  indi- 
cation which  was  strengthened  by  Zeeman's  discovery  in  1897  of  the 
splitting  by  a negative  field  of  a single  spectral  line  into  two  or 
three  lines,  for  this  wnen  worked  out  quantitatively,  pointed  to  the 


• ■ 


. . 


. 


, 


. 


3 


existence  witnin  tne  atom  of  a negatively  cnarged  particle  which  had 
approximately  the  same  value  of  e/m.  Attempts  had  been  first  made 
at  a direct  determination  of  _e  by  Townsend  in  1897,  and  was  followed 
by  J.J.  Thomson,  H. A.  Wilson,  Bogeman  and  Millikan.  The  latrer  ap- 
plied a number  of  methods:  One  of  them  being  the  method  of  obser- 
vation. His  results  are  given  below  in  the  table.  The  table  is 
taken  from  Millikan's  book  entitled  "Tne  Electron":- 

Serles  Charge  Value  of  e Weight  assigned 


1 

3e 

4.59 

7 

2 

4e 

4.56 

7 

3 

2e 

4,64 

6 

4 

5e 

4.83 

4 

5 

2e 

4.87 

1 

6 

6e 

4.  69 

3 

The  study  of  e/m  for  positive  ions  in  exhausted  tubes  tnough 
first  carried  out  quantitatively  by  fien  has  been  elaborately  and 
most  successfully  dealt  with  by  Sir  J.J,  Thomson.  The  results  of  the 
works  of  all  observers  up  to  date  seem  to  show  quite  conclusively 
that  e/m  for  a positive  ion  in  gases  is  never  larger  than  its  value 
for  the  hydrogen  ion  in  electrolysis,  ana  that  it  varies  with  differ- 
ent sorts  of  residual  gases  just  as  it  is  found  to  be  in  electrolysis 

II.  DETERMINATION  OF  e/m 

General  Theory.-  Different  methods  have  been  used  to  deter- 
mine the  ratio  e/m  for  small  particles,  but  most  of  the  calculations 
depend  on  some  experimental  investigations  of  the  effect  of  a mag- 
netic force  on  the  motion  of  the  particle.  The  simplest  case  is 
that  of  a particle  moving  in  a vacuum  in  which  the  electric  force  is 


. 


-f 


4 


zero  and.  tne  magnetic  force  H is  perpendicular  to  tne  direction  of 
the  motion.  If  v be  the  velocity  of  the  particle,  tne  force  hev  act- 
ing on  it  is  in  a direction  at  rignt  angles  to  the  direction  of  tne 
motion  ana  to  tne  magnetic  force,  so  tnat  wnen  H is  constant  tne  par- 
ticle moves  in  a circle  witn  a constant  velocity.  Tne  radius  r of 
tne  circle  is  obtained  by  equating  tne  centrifugal  force  to  tne  force 
Hev  along  tne  normal  to  the  trajectory,  nence: 

mv3/r  = Hev 

or  e/m  = v3/rHv  = v/rH. 

In  a discharge  tube  containing  a gas  at  a very  low  pressure 
tne  electric  force  in  the  neighbornood  of  the  cathode  is  large,  so 
tnat  tne  particles  set  free  from  the  catnode  acquire  a high  velocity 
and  may  penetrate  considerable  distances  without  mucn  loss  of  energy 
by  collision  with  molecules.  If  tne  electrodes  are  fixed  at  one  end 
of  tne  tube,  the  rays  move  witn  a velocity  wmcn  is  approximately 
constant  for  tne  remainder  of  their  path,  and  tne  curvature  1/r  of 
their  trajectory  produced  by  a magnetic  force  may  easily  be  found, 
so  tnat  one  relation  between  tne  two  quantities  e/m  and  v is  tnus  ob- 
tained. If  in  addition  tne  velocity  v is  known,  or  some  otner  rela- 
tion connecting  e/m  and  v,  tne  values  of  botn  of  tnese  quantities  may 
be  obtained. 

In  1890  scnuster  read  a paper  before  the  Royal  Society  in 
which  he  mentioned  tnat  an  upper  limit  and  a lower  limit  for  tne 
ratio  e/m  could  be  establisned. 

He  mentioned  that  particles  are  projected  from  tne  catnode. 
The  observed  effect  of  the  magnet  on  tnem  is  exactly  what  it  should 
be  under  the  circumstances.  The  patn  of  tne  particles  can  be  traced 
by  means  of  tne  luminosity  produced  by  tne  molecular  impacts.  If 


. 


. 


. 

*- 

. 


. 


5 


the  trajectory  is  originally  straight,  it  bends  under  tne  influence 
of  a magnet.  The  curvature  of  the  rays  depends  on  two  unknown 
quantities,  the  velocity  of  tne  particles  and  the  quantity  of  elec- 
tricity tney  carry. 

If  tne  particles  carrying  a cnarge  are  moving  with  velocity 
at  right  angles  to  tne  lines  of  force,  tne  radius  of  curvature  r is 
determined  by  tne  equation 

mv2/r  = Hve 

or  e/m  = v/Hr,  (1) 

where  m is  the  mass  of  the  particle,  ana  H the  magnetic  force.  If 
the  particles  originally  at  rest  start  from  the  cathode  at  which  the 
potential  is  taken  as  zero,  and  arrive  without  loss  of  energy,  at  a 
place  where  the  potential  is  E,  we  should  have  another  equation, 
namely 


2Ee  = mv2,  (2) 

Eliminating  v,  we  find 

e/m  = 2E/H2r2.  (3) 

A lower  limit,  he  mentioned,  can  be  calculated  as  follows: 

As  long  as  the  effect  of  the  magnet  on  the  particles  projected  from 
the  cathode  shows  any  directional  preponder ence,  we  may  take  it  that 
the  velocities  of  the  particles  must  be  greater  than  the  mean  velo- 
city in  their  normal  state.  For  it  is  clear  that,  if  distribution 
of  velocities  was  symmetrical  in  all  directions,  the  magnet  would 
have  equal  and  opposite  effects  on  the  charges  which  move  in  opposite 
directions;  and  if  by  mutual  impact  the  velocity  is  reduced  to  its 
normal  value,  it  will  also  have  lost  any  directional  inequality.  We 
may  obtain  a lower  limit  lor  e/m  if  in  equation  (1)  we  calculate 

e/m  = v/Hr  (4) 


• 

. 

■ 

, 

6 


by  putting  for  r tne  smallest  radius  of  curvature  wnicn  can  witn  cer- 
tainty be  traced  in  tne  glow,  and  for  v the  mean  velocity  of  tne  par- 
ticle, according  to  tne  kinetic  energy  of  gases. 

In  an  actual  experiment  by  Schuster,  H was  200  gausses;  r 
diminished  with  increasing  distance  from  the  cathode.  The  greatest 
value  which  could  with  certainty  be  measured  was  about  1 cm.  E was 
225  volts  at  the  same  place.  Taking  these  numbers  we  get  for  the 
upper  limit 

e/m  11  x 10^ 

and  the  lower  limit  he  got  to  be 

e/m  >1Q5. 

This  lower  limit  for  e/m  as  Schuster  found,  were  very  near 
the  observed  values. 

Wiecnert  Method.-  wiechert,  in  January,  18S7,  first  showed 
that  tne  ratio  e/m  for  a cathode-ray  particle  is  between  4000  and 
2000  times  as  great  as  the  value  of  e/m  corresponding  to  an  atom  of 
hydrogen,  tne  velocity  of  the  cathode  being  in  some  cases  about  one- 
tentn  of  the  velocity  of  light,  he  attributed  tne  large  value  of 
e/m  to  the  smallness  of  the  mass  m and  considered  the  charges  e and 
E to  be  the  same. 

Wiechert,  working  with  rays  in  hydrogen  at  a very  low  press- 
ure, measured  the  curvature  1/r  of  tne  trajectory  produced  by  a known 
negative  force  H,  and  obtained  the  value  of  Hv  for  substitution  in 
the  formula 

e/m  = v/Hr. 

The  velocity  v was  determined  by  a direct  method  in  wmch 
tne  period  of  oscillation  of  a condenser,  discharging  through  a cir- 
cuit of  known  s elf- inductance  was  used  to  estimate  the  short  interval 


h g 

d a 

9 f 

£ ^ 

Figure  i . 


7 


of  time  required  by  the  rays  to  traverse  a given  distance  in  tne  dis- 
charge tube.  This  principle  had  previously  been  used  by  aes  Condres 
who  found  tnat  the  cathode  rays  nad  a velocity  exceeding  2 x 108 
centimeters  per  second.  Guided  by  this  result  Wiechert  designed  an 
apparatus  by  means  of  which  it  was  possible  to  compare  the  time  in 
which  the  rays  traversed  a distance  of  about  20  centimeters  with  the 
period  of  T of  a condenser,  T being  between  10  ° and  10  second. 

The  arrangement  of  apparatus  is  shown  by  the  illustration  of  tne  dis- 
charge tube  (Fig.l).  In  front  of  the  cathode,  K,  and  at  a distance 
25  centimeters  from  it,  he  placed  a plate  of  glass,  G,  that  fluoresced 
brightly  under  the  action  of  the  rays.  Two  metal  screens,  and  Bg, 
were  placed  between  the  catnode  and  the  glass  plate.  The  screen,  Bg, 
was  5 centimeters  from  the  glass  plate  and  had  a slit  in  tne  centre 
a few  millimeters  wide.  The  otner  screen,  B^,  7-1/2  centimeters  from 
the  cathode  extended  across  tne  lower  part  of  the  tube,  ana  its  edge 
was  parallel  to  the  slit  in  Bg.  The  positive  electrode,  which  is 
not  shown  in  tne  figure,  was  in  tne  form  of  a ring  ana  was  placed 
between  tne  cathode  ana  screen  B^.  The  discnarge  was  produced  by  the 
secondary  circuit  of  a Tesla  transformer,  and  the  rays  from  the  cen- 
ter of  the  cathode,  passed  over  the  edge  of  tne  first  screen  and 
througn  the  slit  in  tne  second.  A narrow  fluorescent  strip,  a few 
millimeters  wide,  marJced  tne  points  on  the  surface  of  glass,  (*,  on 
which  the  rays  impinged. 

When  a magnet  was  placed  in  a suitable  position  near  the 
cathode  most  of  the  rays  bent  down  and  fell  on  tne  screen  B]_,  and 
only  a slight  fluorescence  was  seen  on  the  glass  plate. 

Tne  two  wires,  abed,  and  efgn,  formed  part  of  tne  circuit  of 
the  oscillatory  discharge  of  a condenser,  which  was  charged 


* 


8 

inductively  by  tne  Tesla  apparatus  used  to  produce  tne  cathode  rays. 
Thus,  a current  flowed  tnrough  tne  wires  abed  and  at  tne  same  in- 
stant the  high  potential  was  established  between  tne  electrodes. 

When  the  wire  is  brought  close  to  the  tube,  as  shown  in  tne  figure, 
the  magnetic  force  due  to  the  current  in  be  counteracts  tne  effect 
of  tne  magnet,  when  the  cathode  rays  are  emitted,  so  that  some  of 
the  rays  pass  over  tne  edge  of  B^.  An  increase  is  thus  produced  in 
tne  fluorescence  at  G,  due  to  the  rays  wnicn  between  K and  B^,  wnen 
tne  alternating  current  in  tne  condenser  circuit  is  in  a certain 
phase. 

The  effect  of  tne  current  on  the  rays  as  they  pass  from  tne 
slit  in  Bg  to  the  glass  plate  is  tnen  observed  by  bringing  tne  wire 
ef  gh  near  tne  tube.  Let  t be  tne  time  in  which  tne  rays  travel  from 
B1  1 the  Period  of  oscillation  of  the  condenser  discharge;  tner 

if  T is  large  as  compared  with  t_,  the  deflection  produced  by  the  cur- 
rent in  f£  is  in  the  same  direction  as  the  deflection  produced  by  be I 
If  tne  period  of  tne  condenser  discharge  is  reduced  until  f/4  = t, 
the  deflection  produced  between  Bg  and  G becomes  very  small.  Thus, 
by  observing  tne  displacement  of  tne  fluorescence  of  tne  glass  plate 
obtained  by  reducing  the  period,  T,  the  time,  t,  may  be  estimated. 

It  was  thus  faund  tnat  for  rays  for  which  the  value  of  &£ 
was  150,  the  velocity  v was  about  b x 10^  centimeters  per  second}. 

7 

and  the  value  e/m  about  3 x 10  , tne  true  value  being  possibly 
greater  than  these  numbers. 

Weichert  also  considered  tne  possibility  of  determining  e/m 
from  measurement  of  tne  potential  difference,  W,  between  tne  elec- 
trodes. An  upper  limit  of  the  velocity  of  tne  electron  in  tne  tube 
may  be  obtained  on  tne  hypothesis  that  the  rays  start  fram  tne 


* 


A 


. 


. 


9 


negative  electrode  and  move  freely  under  the  electric  force.  The 
maximum  kinetic  energy  acquired  by  the  cnarged  particle  is  then, 

Biv2/  3 = eW, 

ana  e/m  is  given  by  the  equation 

e/m  = v2/2W# 

7 

The  upper  limit  of  tne  value  of  e/m  tnus  obtained  was  4 x 10  . 

Subsequently,  the  arrangement  of  tne  apparatus  for  measuring 

the  velocity  of  tne  rays  was  made;  the  most  probable  values  of  e/m 

were  found  to  be  between 

17  17 

4.b4  x 10  and  6. 04  x 10x  in  electrostatic  units 
and  1.55  x 107  and  1.01  x 107  in  electromagnetic  units, 

Kaufman* s Met nod. - Kaufman  performed  a number  of  experiment  i 
in  1897,  on  the  determination  of  e/m  for  cathode  rays.  He  introduced 
a method  by  wnich  the  deflection  due  to  electric  and  magnetic  force 
takes  place  simultaneously  and  can  be  measured  witn  great  accuracy. 

His  method  depends  on  the  simple  principle  that  in  a gas  at  suffi- 
ciently low  pressures  the  kinetic  energy  acquired  by  the  electrons 
in  passing  from  tne  catnode  to  the  anode  is  eW,  W being  tne  potential 
difference  between  tne  electrodes.  Under  these  conditions,  tne  value 
of  e/m  is  given  by  the  formula 

e/m  = 2W/H3r2, 

r being  the  radius  of  curvature  of  tne  trajectory  in  a transverse 
magnetic  field  H.  This  implies  that  tne  loss  of  energy  of  the  elec- 
trons due  to  collisions  is  very  small,  and  tne  investigations  snow 
tnat  any  sucn  effect  must  have  been  negligible.  Kaufman  made  a 
number  of  experiments  in  which  the  gas  was  at  different  small  press- 
ures, and  the  potential  difference  between  the  electrodes  required 
to  produce  the  discharges  varied  from  bOOO  to  4000  volts.  The 


10 


velocity  was  liaole  to  be  diminisned  appreciably  due  to  the  collision 
between  tne  rays  ana  molecules,  so  if  W aiminishes  error  in  tne  for- 
mulae would  increase.  But  it  was  observed  that  tnere  was  no  appre- 
ciable difference  in  the  value  of  quantity  W/H2r2  for  different 
pressures  at  which  tne  experiments  were  performea.  So  tnat  if  we  tak  i 
eW  as  tne  kinetic  energy  tne  error  wouia  not  be  serious. 

Tne  apparatus  that  Kaufman  usea  is  snown  in  Fig, 3.  Tne 
glass  tube,  R,  11  centimeters  long  and  6.b  centimeters  wide,  was 
closed  witn  a gas  plate,  G,  tne  eiectroaes  K ana  P being  contained  in 
tne  tube  T.  Tne  ca-cnoae  K was  raised  to  a nign  potential  Dy  a Wims- 
nurst  macnine,  and  tne  potential  difference  W between  the  electrodes 
was  measured  by  an  electrostatic  voltmeter.  The  case  of  tne  volt- 
meter and  the  positive  electrode  P were  connected  to  earth.  A thin 
layer  of  cnalk,  wmcn  fluoresced  under  tne  action  of  tne  rays,  was 
spread  over  the  plate  G,  an  electrode  wmcn  was  a platinum  wire  naif 
a millimeter  in  diameter,  cast  a snaaow  on  tne  fluorescent  plate. 

The  magnetic  force  n was  establisned  in  tne  space  between  P ana  G oy 
tne  current  in  tne  solenoid  S.  The  deflection  of  tne  rays  was  meas- 
ured by  tne  displacement  d of  tne  shadow  of  the  wire,  ana  since  d 
was  small  compared  witn  tne  distance  PG,  tne  radius  of  curvature  r 
of  tne  trajectory  was  inversely  proportional  to  d (2rd  = a2 approxi- 
mately, a,  being  tne  distance  PG) . 

Experiments  made  witn  a copper  electrode  at  K gave  tne  fol- 
lowing results: 

With  air  at  different  pressures,,  .03  to  .07  millimeters. 

The  potential  W required  to  produce  the  discharge  varied  from  10630 
v ol 1 8 to  3260  volts,  but  the  quantity  W/Hr  remained  constant,  the 
mean  value  being  proportional  to  393,  398,  406,  in  a series  of 


11 


experiments  in  which  the  cathode  was  placed  at  various  distances 
from  the  wire  P. 

With  coal-gas  the  mean  value  401.5  was  obtained  in  experi- 
ments in  which  W varied  from  6410  to  11850  volts. 

In  hydrogen  and  carbonic  acid  the  quantity  J%/ Hr  was  found 
to  be  proportional  to  404  and  398,  the  potential  difference  W rang- 
ing from  4000  to  14000  volts. 

An  aluminum  cathode  was  also  used  with  air  in  the  tube,  and 
the  results  were  the  same  as  those  obtained  with  the  copper  elec- 
trodes. 

Thus,  the  value  of  e/m  is  independent  of  the  pressure,  the 
distance  between  the  electrodes,  and  the  nature  of  the  gas. 

In  order  to  obtain  an  exact  value  it  was  necessary  to  take 
into  account  the  fact  that  the  field  is  not  absolutely  uniform  and 
to  take  accurate  measurements  of  the  force  H along  the  line  from  P 
to  G due  to  given  current  in  the  coil  S. 

When  the  rays  traverse  a distance  x in  the  transverse  mag- 
netic field,  the  velocity  v at  right  angles  to  the  original  direction 
of  motion  is: 

v — f*  He/m  dx. 


so  that  the  small  deflection  d on  a screen  at  a distance  a from  the 
origin  is 


= e/mv  f dx  f Hdx 
Jo  Jo 

= Je/ 2mW  j d n j Hdx. 


Later,  Kaufman  made  a complete  investigation  of  the  magnetic 


13 


7 

field  and  found  the  value  of  e/m  for  cathode  rays  to  be  1.77  x 10  . 

Simon,  working  with  tne  same  apparatus  as  Kaufmann,  with  sorr  i 

n 

improvements,  found  the  value  of  e/m  to  be  1.8B5  x 10. 

Thomson's  Methods.-  Sir  J.J.  Thomson,  in  1897,  determined 
e/m  by  two  different  and  independent  methods;  and  his  values  are  in 
general  agreement  with  those  obtained  by  Kaufmann  and  Wiechert. 

(a)  First  Method.-  He  considered  a bundle  of  homogeneous 
cathode  rays,  m being  the  mass  of  each  of  the  particles,  _e  the  charge 
N the  number  of  particles  passing  across  any  section  of  the  beam  in 
a given  time;  then  £ the  quantity  of  electricity  carried  by  these 
particles  is  given  by  the  equation: 

Ne  = Q. 

When  these  rays  strike  against  a solid  body  the  temperature  of  the 
body  is  raised;  the  kinetic  energy  of  the  moving  particles  being  con- 
verted into  heat.  If  we  suppose  that  all  this  energy  is  converted 
into  heat,  then,  if  we  measure  the  increase  in  the  temperature  of  a 
body  of  known  thermal  capacity  caused  by  the  impact  of  these  rays, 
we  can  determine  W,  the  kinetic  energy  of  the  particle,  and  if  u is 
the  velocity  of  the  particles, 

l/2Nmv2  = W. 

If  r is  the  radius  of  curvature  of  the  path  of  these  rays  in  a uni- 
form magnetic  field  H,  then 

mv/  e = Hr  = I 

where  I_  is  written  for  Hr  for  the  sake  of  brevity.  From  tnese  equa- 
tions we  get 

l/3v2  m/e  = W/Q 

v = 2W/QI 
m/e  = I2Q/2W. 


therefore 


13 


If  we  know  W and  I,  we  can  deduce  the  value  of  e/m. 

Thomson  used  tubes  of  three  different  types;  the  first  one 
is  represented  in  Fig. 3,  except  that  the  plates  E and  D were  absent. 
Two  coaxial  plates  are  fastened  to  tne  ends  of  the  tube.  The  rays 
from  tne  cathode  _C  fall  on  the  metal  plug  B,  which  is  connected  with 
the  earth,  and  serves  for  the  anode.  A horizontal  slit  is  cut  in  the 
plug  B.  The  cathode  rays  pass  througn  this  slit  and  then  strike 
against  the  two  co-axial  cylinders  at  the  end  of  the  tube.  Slits  are 
cut  in  these  cylinders,  so  that  the  cathode  rays  pass  into  tne  in- 
side of  the  inner  cylinder.  The  outer  cylinder  is  connected  with  the 
earth.  The  inner  cylinder  which  is  insulated  from  the  outer  one,  is 
connected  with  an  electrometer,  the  deflection  of  which  measures  the 
quantity  of  electricity  Q brought  into  tne  inner  cylinder  by  the  rays 
A thermo-electric  couple  is  placed  benmd  the  slit  in  the  inner  cylin  - 
der. This  couple  is  made  of  very  thin  strips  of  iron  and  copper 
fastened  to  very  fine  iron  wires.  These  wires  passed  through  tne 
cylinders,  being  insulated  from  them,  ana  tnrough  the  glass  to  the 
outside  of  tne  tube,  wnere  they  were  connected  with  a low  resistance 
galvanometer.  The  deflection  of  which  gave  data  for  calculating  the 
rise  of  temperature  of  the  junction  produced  by  tne  impact  against 
it  by  the  cathode  rays.  The  strips  of  iron  and  copper  were  large 
enough  to  insure  tnat  every  catnode  ray  which  entered  the  inner 
cylinder  struck  against  the  junction.  In  some  of  the  tubes  the 
strips  of  iron  and  copper  were  placed  end  to  end,  so  that  some  of  the 
rays  struck  against  the  iron  and  others  against  tne  copper.  in  otn- 
ers  the  strip  of  one  metal  was  placed  in  front  of  the  other.  No  dif- 
ference, however,  could  be  detected  between  tne  results  gotten  with 
these  two  arrangements.  The  strips  of  iron  and  copper  were  weighed. 


14 


in  one  set  or  junction 

and  the  thermal  capacityAwas  5 x 10” ^ microfarad,  ana  in  the  other 
3 x 10”*5.  If  we  assume  tnat  tne  catnoae  rays  wmcn  strike  against 
tne  junctions  give  tneir  energy  up  to  it,  tne  deflection  of  tne 
galvanometer  gives  us  W or  l/2Wmv2. 

The  value  of  _I,  i.e..  Hr,  wnere  t is  tne  curvature  of  tne 
patn  of  tne  rays  m a magnetic  field  of  strength  H,  was  found  as 
f ol 1 ows : 


The  tube  was  fixed  between  two  large  circular  coils  placed 
parallel  to  eacn  otner,  and  separated  by  a distance  equal  to  tne  ra- 
dius of  eitner.  These  coils  produced  a uniform  magnetic  field,  the 
strength  of  which  is  gotten  by  measuring  with  an  ammeter  the  strength 
of  the  current  passing  them.  The  cathode  rays  are  thus  in  a uniform 
field,  so  that  their  path  is  circular.  Suppose  that  the  rays  when 
deflected  by  a magnet  strike  against  the  glass  of  the  tube  at  E as 
shown  in  Fig. 4.  Then,  if  x_  is  the  radius  of  circular  path  of  the 
rays. 


2r 


CE5 

AC 


+ AC. 


Then  if  we  measure  CE  and  AC  we  nave  the  means  of  determining  the 
radius  of  curvature  of  tne  path  of  the  rays. 

The  determination  of  r.  is  rendered  to  some  extent  uncertain, 
in  consequence  of  the  pencil  of  rays  spreading  out  under  the  action 
of  the  magnetic  field  sc  that  the  phosphorescent  patch  at  je  is  sev- 
eral millimeters  long.  Thus  values  of  jc  differing  appreciably  from 
each  other  will  be  gotten  oy  taking  E at  different  points  of  this 
phosphorescent  patch.  Part  of  this  paten  was,  however,  generally 
considerably  brighter  than  the  rest.  When  this  was  the  case,  E was 
taken  as  the  brightest  point.  When  such  a point  of  maximum  bright- 
ness did  not  exist  the  middle  of  the  patch  was  taken  for  E.  The 


15 


uncertainty  in  tne  value  of  r tnus  introduced  amounted  sometimes  to 
about  20  per  cent.  By  tnis  it  is  meant  tnat  if  we  take  E first  at 
one  extremity  of  the  patch  and  then  at  the  other,  we  should  get  val- 
ues of  r differing  by  this  amount. 

The  measurement  of  £,  the  quantity  of  electricity  which  ent- 
er® the  inner  cylinder,  is  complicated  by  cathoae  rays,  making  the 
gas  through  wnicn  they  pass  a conductor,  so  that  though  the  insu- 
lation of  the  inner  cylinder  was  perfect  when  the  rays  were  off,  it 
was  not  so  when  they  were  passing  through  tne  space  between  the  cylin  - 
ders.  This  caused  some  of  the  charge  communicated  to  the  inner 
cylinder  to  leak  away,  so  that  the  actual  charge  given  to  the  cylin- 
der by  the  cathode  rays  was  larger  than  that  indicated  by  tne  elec- 
trometer. To  make  tne  error  from  this  cause  as  small  as  possible, 
the  inner  cylinder  was  connected  to  the  largest  capacity  available, 

1.5  microfarads,  and  the  rays  were  only  kept  on  for  a snort  time, 
about  one  or  two  seconds,  so  that  the  alteration  in  potential  of  the 
inner  cylinder  was  not  large,  ranging  in  the  various  experiments  from 
about  .5  to  5 volts,  another  reason  why  it  is  necessary  to  limit  the 
duration  of  the  rays  to  as  short  a time  as  possible,  is  to  avoid  the 
correction  for  the  loss  of  heat  from  tne  thermo-electric  junction  by 
conduction  along  tne  wires.  The  rise  in  temperature  of  the  junction 
by  conduction  was  of  the  order  2°C.  a series  of  experiments  showed 
that  with  the  same  tube  and  the  same  gaseous  pressure,  £ and  W were 
proportional  to  each  other  when  the  rays  were  not  kept  on  too  long. 

Tubes  of  this  kind  gave  satisfactory  results.  The  chief 
drawback  being  that  sometimes  in  consequence  of  the  charging  of  the 
glass  walls  of  the  tube,  a secondary  discharge  starfed  from  the 
cylinder  to  the  walls  of  tne  tube,  ana  the  cylinders  were  surrounded 


Fig.  5- 


16 


by  a glow.  When  this  glov;  appeared,  the  readings  were  very  irregular 
The  glow  could,  nowever,  be  gotten  rid  of  by  pumping  ana  letting  the 
tube  rest  for  some  time.  The  results  gotten  with  this  tube  by  Sir. 
J.J.  Thomson  are  given  in  Table  I. 

The  second  type  of  tube  was  like  the  one  shown  in  Fig. 5.  A 
double  cylinaer  with  a thermo-electric  junction  like  those  used  in 
the  previous  tube  were  placed  in  the  line  of  fire  of  the  rays.  The 
inside  of  the  bell  jar  was  lined  with  copper  gauge  connected  with  the 
earth.  This  tube  gave  very  satisfactory  results.  There  never  ap- 
peared any  glow  around  the  cylinders,  and  the  readings  were  more  con- 
cordant. The  only  drawback  was  that  some  of  the  connections  had  to 
be  made  with  sealing  wax,  ana  hence  it  was  not  possible  to  get  the 
highest  exhaustion  with  this  tube  so  that  tne  range  of  pressure  was 
less  than  that  for  tube  wo. 1.  The  results  gotten  with  this  tube  are 
given  in  Table  II. 

The  third  type  of  tube  used  by  Sir  J.J.  Thomson  was  similar 
to  the  first  one  except  that  the  openings  in  the  two  cylinders  were 
made  very  much  smaller.  In  this  tube  the  slits  in  the  cylinders  were 
replaced  by  small  noles  about  1.5  millimeters  in  diameter.  In  con- 
sequence of  the  smallness  of  the  openings  the  magnitude  of  the  ef- 
fect was  very  much  reduced.  In  order  to  get  measureable  results,  it 
was  necessary  to  reduce  the  capacity  of  the  conaenser  in  connection 
with  the  inner  cylinder  to  .15  microfarad,  ana  to  make  tne  galva- 
nometer exceedingly  sensitive,  as  the  rise  in  temperature  of  the 
thermo-electric  junction  was  in  these  experiments  only  about  .5°C  on 
the  average.  Tne  results  obtained  in  this  tube  are  given  in  Table 
III. 

It  will  be  noticed  that  the  value  of  m/e  is  greater. 


. 

, 

. 


17 


TABLE  I 


Gas 

Value  of 
W/Q 

I 

air 

4.6X1011 

230 

air 

l.BxlO12 

350 

air 

S.lxlO11 

230 

air 

2.5xl012 

400 

air 

5. 5X1011 

230 

air 

1 P 

l.oxicr 

285 

air 

l.OxlO12 

285 

hydrogen 

6. OxlO12 

205 

hydrogen 

2. lxlO12 

460 

card Ohio 
acid 

8.4X1011 

260 

carbonic 

acid 

1. 4?xl012 

340 

carbonic 

acid 

3. OxlO12 

480 

m/e 

e/m 

V 

.57xl0”7 

1.  75xl07 

4. OxlO9 

. 34xl0”7 

2, 94xl07 

1. OxlO1 

. 43x1 0”7 

2. 33xl07 

5. 4x1 09 

. 32x1 0”7 

3. 12x1 07 

l.BxlO1' 

. 48x10” 7 

2. 08x1 07 

4.  8xl09 

. 40x10” 7 

2. 5x1 07 

7.  OxlO9 

. 40x1 0”7 

2. 5xl07 

7.  OxlO9 

. 35xl0~? 

2. 86xl07 

6. OxlO9 

. 50xl0”7 

2. OxlO7 

9. 2x1 09 

. 40x10” 7 

2. 5x1 07 

7. 5x10® 

. 40xl0”? 

2. 5xl07 

8. 5xl09 

. 39x10” 7 

2.57xl07 

1.3X101 

17a 


TABLE 

II 

gas 

value  of 
W/Q 

I 

m/  e 

e/m 

V 

air 

3.  8xlOn 

175 

,53xl0”7 

1. 89xl07 

3.3x10^ 

air 

4.4X1011 

195 

. 47xl0”7 

2. 13xl07 

4.1x10' 

air 

b.SxlO11 

181 

. 47xlO"7 

3.13xl07 

3.8x10' 

hydrogen 

3. 8X1011 

175 

. 53x10*" 7 

1. 89xl07 

3.  3x10’ 

air 

3.5X1011 

160 

.51xl0”7 

1. 96xl07 

3.1x10' 

carbonic 

acid 

3. OxlO11 

148 

. 54xl0~7 

1.85xl07 

2. 5x10* 

air 

1.8X1011 

151 

. 63x1 0"7 

1. 59xl07 

2.  3x1 0^ 

hydrogen 

3. 8x1 011 

175 

. 53x10” 7 

1. 89xl07 

3.  3x10' 

hydrogen 

4. 4X1011 

301 

. 46xl0”7 

2. 18xl07 

4.4x10' 

air 

3.5xlOU 

176 

. 61xl0~7 

1 . 64xl07 

2.8xl0! 

air 

4. 3X1011 

300 

. 48xl0”7 

3.08xl07 

4. 1x10' 

TABLE 

Ill 

gas 

air 

value  of 
W/Q 

2.5X1011 

I 

330 

m/  e 

90xl0”7 

e/m 

l.llxlO7 

V 

2. 4xl09 

air 

3.5X1011 

235 

70xl0”7 

1.43xl07 

5.3xl09 

hydrogen 

3. OxlO11 

350  1. 

OOxlO*"7 

1. OOxlO7 

3.5xl09 

18 


considerably,  for  tube  No. 3 than  for  Tubes  No.l  and  2.  In  tube  No.  3 
the  opening  is  a small  nole  ana  in  No.l  and  2 in  is  a slit  of  much 
greater  area.  The  values  of  m/e  gotten  from  tube  No.l  and  2 are  too 
small,  in  consequence  of  leakage  from  tne  inner  to  the  outer  cylinder 
by  tne  gas  being  rendered  a conductor  by  the  passage  of  the  cathode 
rays. 

It  will  also  be  noticed  that  the  value  of  m/e  is  independent 
of  tne  nature  of  the  gas.  Thus,  for  the  first  tube  the  mean  for  tne 
air  is  .4  x 107 , for  hydrogen,  .42  x IQ7  , and  for  carbonic  acid  gas 
. 4 x 107. 

For  the  second  tube  the  mean  value  of  m/e  for  air  is  .52  x 

-7  -7  -7 

10  , for  hydrogen  .50  x 10  , and  for  carbonic  acid  gas  .54  x 10  . 

(b)  Second  Met  nod  of  Sir  J.J.  Thomson.-  This  method  is 
based  upon  the  simultaneous  deflection  of  cathode  rays  in  an  electro- 
static field  and  in  a magnetic  field.  If  the  deflection  experienced 
by  tne  rays  when  traversing  a given  lengtn  under  a uniform  electric 
intensity,  and  the  deflection  of  the  rays  when  tney  traverse  a given 
distance  under  a uniform  magnetic  field,  are  measured,  the  values  of 
e/m  and  v can  be  found  in  the  following  way: 

Let  the  space  passed  over  by  the  rays  under  a uniform  elec- 
tric intensity  F be  1_,  the  time  taken  by  the  rays  to  traverse  this 
space  is  1/v,  the  velocity  in  tne  direction  of  F is  therefore 

Fe  ^ 1 
m * v 

so  that  0,  the  angle  through  wmcn  tne  rays  are  deflected  when  they 
leave  the  electric  field  ana  enter  a region  free  from  electric  force 
is  given  by  the  equation 

_ Fe  1 . 

0 “ m • v^ 


19 


If,  instead  of  the  electric  intensity,  the  rays  are  acted  on  oy  a 
magnetic  force  H at  right  angles  to  the  rays,  and  extending  across 
the  distance  .1,  the  velocity  at  right  angles  to  tne  original  path  of 
tne  rays  is  ■ . y , so  that  <f>  , tne  angle  tnrough  which  tne  rays 
are  deflected  wnen  tney  leave  tne  magnetic  field,  is  given  by  tne 
equation 

6 = He  1 . 

' gi  * v 


From  tnese  equations  we  get 


and  _e  _ F_  1 . 

m “ 0 * H2  ‘ 1 

In  tne  actual  experiment  ft  is  adjusted  so  tnat  9 = <f>.  In 
tnis  case  tne  equation  becomes 


and 


e _ £0_  . 

m H21 


The  apparatus  used  in  tnis  experiment  is  represented  in 
Fig. 6.  The  electric  field  is  produced  by  connecting  tne  two  alumi- 
num plates  to  tne  terminals  of  a battery  of  storage  ceils.  The  phos- 
phorescent paten  at  tne  end  of  tne  tube  is  deflected  ana  tne  deflec- 
tion measured  by  a scale  pasted  on  tne  end  of  tne  tube.  As  it  was 
necessary  to  darken  tne  room  to  see  the  pnospnorescent  patQh,  a 
needle  coated  witn  luminous  paint  was  placed  so  tnat  by  a screw  it 
could  be  moved  up  ana  down  tne  scale.  This  needle  could  be  seen 
when  the  room  was  darkened,  ana  it  was  moved  until  it  coincided  witn 
tne  pnospnorescent  patch.  Thus,  wnen  light  was  admitted  the  deflec- 
tion on  the  pnospnorescent  patch  could  be  measured. 


. 


20 


The  magnetic  field  is  produced  by  placing  outside  tne  tube 
two  coils  wnose  diameter  is  equal  to  the  length  of  tne  plates.  The 
coils  are  so  placed  so  tnat  tney  cover  tne  space  occupied  by  tne 
plates,  me  distance  between  tne  coils  is  equal  to  tne  radius  of 
eitner.  The  mean  value  of  the  magnetic  force  over  tne  lengtn  is 
determined  in  tne  following  way: 

A narrow  coil  0 whose  lengtn  is  1,  connected  witn  a bal- 
listic galvanometer,  is  placed  between  the  coils.  Tne  plane  of  tne 
windings  of  jC  is  parallel  to  the  planes  of  tne  coils.  The  cross- 
section  of  tne  coil  is  a rectangle  5 cm.  by  1 cm. 4 With  a given  cur- 
rent sent  tnrough  the  outer  coils,  the  kick  of  tne  galvanometer  is 
observed  when  this  current  is  reversed.  The  coil  C:  is  then  placed 
at  the  center  of  the  two  very  large  coils,  so  as  to  be  in  a field  of 
uniform  magnetic  force.  The  current  through  the  large  coil  is  re- 
versed and  the  kick  of  the  galvanometer  is  again  observed.  By  com- 
paring both  kicks,  first  one  called^,  and  the  second  one /3  , tne  mea 
value  of  the  magnetic  force  over  a lengtn  1 is  gotten.  This  was 
found  by  Sir  J. J.  Thomson  to  be  bQ  x i wnere  _i  is  tne  current  flowing 
through  the  coils.  Thomson  maue  a series  of  experiments  to  see  if 
tne  electrostatic  deflection  was  proportional  to  tne  electric  intens- 
ity between  tne  plates.  This  was  found  to  oe  tne  case. 

The  results  obtained  by  Thomson  are  given  in  tne  following 


L 


table,  he  adjusted  tne  current  through  tne  coils  so  that  tne  electro- 
static deflection  was  tne  same  as  the  magnetic. 


. 


, 


. 


. 


. . 


21 


gas 

0 

H 

F 

1 

m/e 

e/m 

V 

air 

8/110 

5.5 

1.5  x 1010 

5 

1.5  xllO“7 

.77  x 107 

2.8  xlO* 

air 

9.5/110 

5.4 

1.5 

5 

1.1 

.91 

2.8 

air 

15/110 

b.  b 

1.5 

5 

1.2 

. 85 

2,  5 

hyarogen 

9/110 

b.  5 

1.5 

5 

1.5 

.67 

2.5 

carbonic 

acid 

11/110 

b.  9 

1.5 

5 

1.5 

• b? 

2.2 

air 

b/110 

5.0 

1.8 

5 

1.5 

.77 

2. 6 

air 

7/110 

5.6 

1.0 

5 

1.1 

.91 

2.8 

The  cathoae  in  the  first  five  experiments  was  aluminum.  In 
the  last  two  experiments  it  was  maae  01  platinum,  in  the  last  ex- 
periment Sir  William  Crookes'  metnod  of  getting  rid  of  the  mercury- 
vapor  by  inserting  tubes  of  pounded  sulphur,  sulphur  iodide  and  cop- 
per filings  between  the  bulb  and  the  pump  was  adopted.  In  the  calcu- 
lation of  e/m  and  v,  no  allowance  has  been  made  for  the  magnetic 
force  due  to  the  coil  in  the  region  outside  the  plates.  In  this  re- 
gion the  magnetic  force  will  be  in  the  opposite  direction  to  that  be- 
tween the  plates,  and  will  tend  to  bend  the  cathode  rays  in  the  op- 
posite direction.  Thus  the  effective  value  of  H will  be  smaller 
than  the  value  used  in  the  equations  so  that  the  values  of  m/ e are 
larger  and  those  of  v much  less  than  they  would  be  if  this  correc- 
tion is  applied. 

It  will  be  seen  from  these  determinations  that  the  value  of 
m/ e is  independent  of  the  nature  of  the  gas,  and  that  its  value, 

4. 

10  , is  very  large  as  compared  with  the  value  10~  , which  is  the 

largest  value  of  this  quantity  previously  known,  and  which  is  the 
value  for  tne  hydrogen  ion  in  electrolysis. 

The  same  method  as  described  above  has  been  used  a number 


22 


of  times  in  the  laboratory  of  physics  at  the  University  of  Illinois, 
by  Professor  C.T.  Knipp,  The  following  results  were  obtained  by 
three  members  of  the  graduating  class  of  1921,  under  his  supervision. 

TABLE  IV  * 


Time 

PD  I Is 

y 

z 

z2 

V 

e/m 

P 

2.25 

328.0  .183  .0335 

1.25 

1.75 

6.  06 

3.10 

X 

109 

1.97xl07 

. 00692 

2.32 

327.6  .180  .0324 

1.275 

1.80 

3.24 

3.01 

X 

109 

1. 75xl07 

.0078 

2.39 

327.2  .181  .0326 

1.325 

1.85 

3.41 

2.96 

X 

109 

1. 75xl07 

.0088 

2.46 

326.8  .175  .0306 

1.42 

1.90 

3.  61 

3.93 

X 

109 

1. 82xl07 

.00988 

2.53 

326.4  .182  .0331 

1.50 

2.00 

4.00 

2.80 

X 

109 

1. 68xl07 

.0106 

3.00 

326.0  .182  .0331 

1.50 

2.05 

4.3 

2.81 

X 

109 

1. 69x10? 

.01116 

3,07 

325.6  .182  .0331 

1.55 

2.10 

4.41 

2.85 

X 

109 

1.70xl0V 

.0118 

3.14 

325.3  .183  .0335 

1.56 

2.15 

4.61 

2.89 

X 

109 

1. 89xl07 

. 01204 

3.21 

325.0  .183  .0335 

1.60 

2.20 

4.84 

3.88 

X 

109 

1. 87xl07 

.01268 

3.28 

324.6  .180  .0324 

1.60 

2.20 

4.84 

2.93 

X 

109 

1.98xl07 

.01312 

3.35 

324.3  .180  .0324 

1.62 

2.2 

4.84 

2.91 

X 

109 

1. 90xl07 

.01380 

3.42 

324.0  .176  .0310 

1.725 

2.2 

4.84 

2.78 

X 

109 

*7 

1.87x10 

. 01428 

3.49 

323.5  .175  .0306 

1.75 

2.2 

4.84 

2.75 

X 

109 

1. 80xl07 

.01476 

3.56 

o23. 3 .181  .0326 

1.80 

2.2 

4.84 

2.58 

X 

109 

1. 71xi07 

. 01508 

4.03 

.175  .0306 

1.85 

2.15 

4.61 

2.54 

X 

109 

1. 69xl07 

. 01508 

Another  i 

set  of 

data 

taken  on  a different  date. 

2.05 

324.  .187  .035 

1.05 

1.70 

2.89 

3.30 

X 

109 

1. 74xl07 

.0040 

2.15 

322.8  .1865.0347 

1.18 

1.80 

3.24 

2.95 

X 

109 

1. 75xl07 

.0067 

2.25 

321.6  .1865.0347 

1.35 

1.875  3.53 

2.82 

X 

109 

1, 66x10? 

.0085 

2.  35 

320. 4 . 1865  .0347 

1.45 

1.90 

3.61 

2.67 

X 

109 

1.77xl07 

.0100 

2.45 

319.2  .1865  .0347 

1.55 

2.00 

4.00 

2.62 

X 

109 

1. 85xl07 

.0112 

2.55 

317.  .1865  JD347 

1.60 

2.05 

4.20 

3.51 

X 

109 

1. 67xl07 

.0116 

23 

While  in  the  process  of  taking  this  data  something  went 
wrong  and  so  after  waiting  a short  time  a new  set  of  data  was  taken. 
The  same  is  given  below: 


Time 

PD 

I 

I3 

y 

z 

z2 

V 

e/m 

9 

3.25 

317. 

.1865 

.0347 

.90 

1.65 

2.  72 

3. 72xl09 

1.91xl07 

.0048 

3.35 

317. 

.1865 

.0347 

1.05 

1.70 

2.89 

3. 29xl09 

1.81xl07 

.0050 

3.45 

317. 

.1865 

.0347 

1.10 

1.75 

3.  06 

3.09X109 

1. 77xl07 

.0056 

3.55 

317. 

.1865 

.0347 

1.15 

1.80 

3.24 

3.12x10s 

1. 75xl07 

.0071 

4.05 

317. 

.1865 

.0347 

1.20 

1.85 

3.41 

3.06xl09 

1. 775xl07 

.0081 

III.  DETERMINATION  OF  e/m  FOR  PARTICLES  SET  FREE  BY  ULTRA  VIOLET 
LIGHT,  AND  FOR  THE  NEGATIVELY  CHARGED  PARTICLES  EMITTED  BY  INCAN- 
DESCENT SOLIDS 

(a)  Lenard's  Method.-  The  earlier  investigations  of  the 
negatively  charged  particles  obtained  by  different  methods  in  gases 
at  low  pressures  show  that  the  ratio  e/m  was  probably  exactly  the 
same  in  all  cases.  Lenard  in  1900,  using  a similar  method  to  that 
of  Xaufmann,  determined  the  ratio  of  the  charge  to  the  mass  of  a 
particle  set  free  by  the  action  of  the  Ultra-violet  light  from  a 
metal  surface,  and  obtained  the  number  1.15  x 107.  His  apparatus  is 
shown  in  Fig. 7. 

A is  an  aluminum  plate  on  which  the  ultra-violet  light 
shines.  This  light  comes  from  a spark  between  zinc  electrodes  and 
enters  tne  tube  through  tne  quartz  window,  B.  E is  another  metal 
electrode  perforated  in  the  middle  and  connected  with  the  earth.  It 
shields  the  right  hand  apparatus  from  tne  electrostatic  action  of 


34 


the  charged  electrode,  A.  D and  £ are  electrodes  which  can  be  con- 
nected witn  an  electrometer.  When  A is  cnarged  up  a stream  of  nega- 
tive electricity  goes  through  the  opening  in  E and,  striking  against 
the  plate  D,  charges  up  the  electrometer  with  negative  electricity. 

If  the  electrometer  be  connected  with  £ instead  of  with  D,  it  will 
net  receive  any  charge.  A charge,  however,  can  be  given  to  £ by  de- 
flecting the  stream  of  negative  ions  by  means  of  a magnet  until  they 
strike  against  £.  As  we  still  further  increase  the  magnetic  field, 
the  ions  will  be  deflected  by  the  field  past  £,  and  the  charge  com- 
municated to  £ will  fall  off  rapidly.  The  amount  of  negative  elec- 
tricity received  by  the  electrodes  D and  £ respectively,  as  the  mag- 
netic force  is  increased,  was  in  Lenard's  experiments  represented  by 
the  curves  in  Fig. 8.  The  ordinates  are  the  charges  received  by  the 
electrodes  ana  the  aoscissae  are  the  values  of  the  magnetic  force. 

The  curve  to  the  left  is  for  the  electrode  D,  that  to  the  right  for 
£.  Since  the  negative  ions  are  not  exposed  to  any  electric  field  in 
the  part  of  the  tube  to  the  right  of  E3,  their  paths  in  this  region 
under  a constant  negative  field  will  be  circles  whose  radii  are  equal 
to  mv/eH.  £ will  receive  the  minimum  charge  when  the  circle  with 
this  radius  passing  through  the  middle  of  the  hole  in  E,  and  having 
its  tangent  horizontal  at  this  point,  passes  also  through  the  middle 
of  the  electrode  0.  The  radius  R of  this  circle  is  fixed  by  the 
relative  positions  of  E and  £.  Hence,  if  we  measure  H when  £ re- 
ceives its  maximum  charge,  we  have 

R = mv/eH.  (1) 

Reiger  found  for  the  negative  ions  emitted  by  glass  when 
exposed  to  ultra-violet  light,  values  of  e/m  ranging  from  9.6  x 10 
to  1.2  x 107. 


. 


. 


25 


(b)  Sir  J.J.  Thomson’s  Method..-  Elster  ana  Geitel  have 
shown  that  tne  rate  of  escape  of  negative  electrification  at  low 

pressure  is  much  diminished  by  magnetic  force  if  the  lines  of  mag- 

at 

netic  force  areAright  angles  to  the  lines  of  electric  force..  Let  us 
consider  wnat  effect  a magnetic  force  would  have  on  the  motion  of  a 
negatively  electrified  particle.  Let  the  electric  force  be  uniform 
and  parallel  to  the  axis  of  x,  while  the  magnetic  force  is  also  uni- 
form ana  parallel  to  tne  axis  of  _z.  Let  tne  pressure  be  so  low  that 
the  mean  free  path  of  the  particles  is  long  as  compared  witn  tne  dis 
tance  tney  move  while  under  observation,  so  that  we  may  leave  out  of 
account  the  effect  of  collisions  on  the  movements  of  the  particles. 

If  m is  the  mass  of  a particle,  e.  its  charge,  X tne  elec- 
tric force,  H tne  magnetic  force,  the  equations  of  motion  are: 

Mfx  _ y Hedy 

and 

mdsy  _ tt  dx  . 
dt2  " nedt 

Eliminating  x we  have 

m 77^3  =lr  'Ue-iie 


The  solution  of  tnese  equations  if  x,y,  dx/dt,  dy/dt  all  vanish  wnen 


t;  is  zero,  is  expressed  by 

Xm 
eB2 


y = | 


-sxn^j 


X = 


Xm 

eH2 


cos 


Hte 


m 


1 


The  equations  show  that  the  path  of  tne  particles  is  a cy- 

cloid,  the  generating  circle  of  which  has  a diameter  equal  to  , 

eH2 

and  rolls  on  the  line  X = 0. 


26 


Suppose  now  that  we  have  a metal  plate  AB  exposed  to  ultra 
violet  light,  placed,  parallel  to  a large  metal  plate  £D  perforated 
so  as  to  allow  the  lignt  to  pass  tnrougn  it  and  fall  upon  the  plate 
AB.  See  Fig. 9.  Then  if  CD  is  at  a higher  electric  potential  tnan 
AB,  tne  particles  travel  along  the  lines  of  electric  force.  Let  us 
now  suppose  that  a uniform  magnetic  force  equal  to  h ana  at  right 
angles  to  the  electric  force  acts  on  tne  particles.  These  particles 


will  now  describe  a cycloid  ana  will  reacn  a distance 


3Xm 

eH3* 


Every 


particle  whicn  leaves  AB  will  reacn  £D  provided  CD  stretcnes  forward 
enougn  to  prevent  tne  particles  passing  hy  on  one  side,  now,  tne 
distance  parallel  to  jr  tnrougn  wnich  tne  particles  have  travelled 
wnen  it  is  at  tne  greatest  distance  from  AB  is  gjto  . hence,  if  CD 
stretches  beyond  AB  by  this  distance  at  least,  all  tne  particles 
will  be  caugnt  by  CD  ana  tne  magnetic  field  will  produce  no  dimin- 
ution in  the  rate  of  leak  between  AB  and  _CD.  If,  on  the  other  hand, 
tne  distance  between  the  plates  is  greater  tnan  then  a particle 

starting  from  AB  will  turn  back  before  it  reaches  CD.  It  will  thus 
never  reach  it,  ana  tne  rate  at  which  CD  acquires  negative  electri- 
fication will  be  diminished  by  the  magnetic  force,  hence,  if  this 
view  of  the  action  of  the  magnetic  field  is  correct,  and  if  we  begin 
with  tne  plates  very  near  together,  and  gradually  increase  the  dis- 
tance between  them,  we  should  expect  that,  at  first  with  the  plates 
quite  close  together,  the  rate  at  which  CD  received  a negative 
charge  would  not  be  effected  by  the  magnetic  force,  but  as  soon  as 
the  distance  between  the  plates  is  equal  to  the  magnetic  force 
will  greatly  diminish  tne  rate  at  whicn  CD  receives  a negative  charge 
and  will  in  fact  reduce  tne  rate  almost  to  zero  if  all  tne  negatively 
electrified  particles  came  from  the  surface  of  AB.  hence,  if  we 


. 

*"S 


. 


V 


* 


• , 


27 

measure  the  distance  between  the  plates  when  the  magnetic  force  first 

diminishes  the  rate  at  which  CD  receives  a negative  cnarge,  we  shall 

determine  the  value  of  and  we  can  easily  determine  X and  H,  and 

eH2  “ 

from  tnem  the  value  of  e/m  can  be  deduced. 

In  the  apparatus  shown,  AB  is  a carefully  polished  zinc 
plate  about  one  centimeter  in  diameter;  while  CD  is  a grating  com- 
posed of  very  fine  wires  crossing  each  other  at  right  angles,  the 
ends  being  soldered  into  a ring  of'  metal.  The  wires  form  network 
with  a mesh  about  one  millimeter  square.  This  is  placed  parallel 
to  AB  on  the  quartz  plate  EF  which  is  about  four  millimeters  thick. 
The  grating  was  very  carefully  insulated.  The  sy stern  is  enclosed 
in  a glass  tube  which  is  connected  with  a mercury  pump  provided 
with  a McLeod  gauge.  The  ultra  violet  light  is  supplied  from  an 
arc  about  three  millimeters  long  between  zinc  terminals.  The  induc- 
tion coil  giving  the  arc  is  placed  in  a metal  box,  ana  the  light  is 
placed  through  a window  cut  in  the  top  of  the  box.  Over  this  window 
the  quartz  base  of  the  vessel  is  placed.  A piece  of  wire  gauze 
connected  with  the  earth  is  placed  between  the  quarts  and  the  win- 
dow. The  plate  AB  is  carried  by  the  handle  L which  passes  through 
a sealing-wax  stopper  in  the  tube  K,  The  magnet  used  is  an  electro- 
magnet of  the  horse  shoe  type.  The  magnetic  force  due  to  magnet  is 
determined  by  observing  the  deflection  of  a ballistic  galvanometer 
when  an  exploring  coil,  of  approximately  the  same  vertical  dimen- 
sions as  the  distance  between  the  plates  AB  and  CD  was  withdrawn 
from  between  its  poles.  The  coil  is  carefully  placed  so  as  to  oc- 
cupy the  same  part  of  the  magnetic  field  as  that  occupied  by  the 
space  between  AB  and  _CD  when  the  magnet  was  used  to  affect  the  rate 
of  leak  of  electricity  between  AB  and  CD.  In  this  way  the  intensity 

of  the  magnetic  iield  between  the  poles  of  the  magnet  was  determined 


28 

by  Thomson  for  a series  of  values  of  the  current  through  the  magnet- 
izing coils  of  the  electromagnet  ranging  between  1 ana  4.5  amperes, 
and  a curve  was  drawn  wnicn  gave  the  magnetic  force  wnen  tne  magnet- 
izing current  read,  by  an  ammeter  was  known. 

The  pressure  of  the  gas  in  the  tube  containing  the  plate  is 
reduced  by  tne  mercury  pump  to  1/100  of  a millimeter  of  mercury.  The 
rate  of  leak  of  negative  electricity  to  CD  when  AB  was  exposed  to 
ultra-violet  light  is  measured  by  an  electrometer.  The  zinc  plate 
is  connected  witn  the  negative  pole  of  a battery  of  small  storage 
cells.  The  positive  pole  of  which  is  put  to  earth.  One  pair  of  the 
quadrants  of  the  electrometer  is  kept  permanently  connected  with  the 
earth.  The  other  pair  is  connected  with  the  wire  gauze  CD.  Initial- 
ly the  two  pairs  of  the  quadrant  are  connected  together;  the  connec- 
tion is  then  broken  and  the  ultra-violet  light  is  allowed  to  fall  on 
the  zinc  plate.  The  negative  charge  received  by  the  w[ire  gauze  in  a 
given  time  is  proportional  to  tne  deflection  of  the  electrometer  in 
that  time.  By  this  method  the  following  results  were  obtained  by 
Thomson,  When  the  difference  of  potential  between  the  illuminated 
plate  and  the  wire  gauze  was  greater  than  a certain  value  depending 
upon  the  intensity  of  the  magnetic  force,  ana  the  distance  between 
AB  and  CD,  no  diminution  in  the  deflection  of  the  electrometer  was 
produced  by  the  magnetic  field,  in  fact  in  some  cases  the  deflection 
was  just  a little  greater  in  the  magnetic  field. 

The  negative  ions  travelling  between  the  plates  will  disturb 
to  some  extent,  the  uniformity  of  the  field  between  the  plates.  But 
if  the  intensity  of  the  ultra-violet  light  is  not  too  great,  so  that 
the  rate  of  the  leakage  and  the  number  of  ions  between  the  plates  is 
not  large,  this  want  of  uniformity  will  not  be  important. 


• 

. 

‘ 

' 

. 

. 

. 

■ 

■ 


. 


29 


Following  is  a specimen  of  Observations: 

Distance  between  the  plates  .29  centimeters 

Strength  of  the  magnetic  field  164  units 


Pressure 

P.  D.  between  poles 
in  volts 


240 

120 

80 

40 


1/100  millimeter 

Deflection  of  electrometer 
in  50  seconds 
Magnet  off  Magnet  on 


180 

160 

160 

150 


190 

165 

140 

75 


These  observations  showed  that  the  critical  value  of  tne  po- 
tential difference  was  about  80  volts.  A series  of  observations  was 
then  made  with  potential  difference  increasing  from  80  volts  by  two 
volts  at  a time,  and  it  was  found  that  90  volts  was  the  largest  poten- 
tial difference  at  wmch  any  effect  due  to  tne  magnet  could  be  de- 
tected. The  results  of  a numoer  of  experiments  are  given  in  the  fol- 
lowing table: 


d (in  cm. ) 

H 

V (in  absolute 
measurement) 

e/m 

.18 

170 

40 

X 

108 

8.  b 

x 1G6 

.19 

170 

50 

X 

108 

5.8 

x 106 

. 20 

181 

46 

X 

00 

o 

rH 

7.1 

x 106 

.29 

16? 

84 

X 

M 

O 

00 

7.1 

x 106 

.29 

164 

90 

X 

O 

00 

7.6 

x 106 

. 50 

160 

86 

X 

M 

O 

00 

7.4 

x 106 

.45 

100 

80 

X 

M 

O 

00 

7.9 

x 106 

The 

mean  ■ 

value  for 

e/m  is 

7.3  x 

106. 

The  value  of  e/m  in  case  of  tne  convection  of  electricity 
under  tne  influence  of  ultra-violet  lignt  is  of  tne  same  order  as  in 
tne  case  of  tne  catnode  rays,  and  is  very  different  from  tne  value  of 
e/m  in  tne  case  of  hydrogen  ions  in  ordinary  electrolysis  which  is 
equal  to  10^.  The  value,  _e,  is  tne  same,  nence  the  mass  must  be  dif- 
ferent and  is  of  tne  order  of  1/1000  of  nydrogen  ion. 

Tnomson  conducted  experiments  on  tne  determination  of  e/m 
for  tne  negative  ion  produced  by  an  incandescent  wire,  nis  metnod 
was  tne  same  as  descrioed  above  in  case  of  ultra-violet  lignt  fall- 
ing on  a plate.  He  found  tne  value  of  e/m  to  be  8.7  x 10^. 

Owen  determined  tne  value  of  e/m  for  tne  particles  emitted 
by  a glowing  Nernst  filament.  He  found  tne  value  to  be  b.bb  x 10^ 
and  for  tnose  emitted  by  glowing  lime  Wennelt  found  tne  value  of  e/m 
to  be  1.4  x id7, 

IV.  M.  and  MADAME  CURIE’S  INVESTIGATIONS  CON- 
CERNING RADIOACTIVE  SUBSTANCES 
M.  and  Madame  Curie  nad  shown  tnat  tne  radioactive  suostanc^ 
radium  emits  negative  ions.  Becquerel  determined  the  velocity  of 
tnese  ions  and  the  value  of  e/m.  His  method  was  based  upon  tne  de- 
flection of  tne  rays  produced  by  an  electrostatic  and  also  by  a mag- 
netic field.  Tne  pressure  was  atmospheric,  ana  the  resistance  of- 
fered to  tne  motion  of  tne  ions  by  tne  gas  through  which  they  pass 
was  neglected.  The  case  cannot  be  justified  but  for  ions  emitted  by 
radium,  as  they  are  very  much  more  penetrating  than  those  tnat  nave 
been  hitherto  considered,  ana  are  able  to  travel  as  far  tnrougn  a 
gas  at  atmospheric  pressure  as  others  at  low  pressure.  so  tne  value 
of  v and  e/m  by  this  method  would  be  right  if  the  resistance  of  tne 


. 


- 


. 


. 


' 

\ 


gas  is  neglected. 


V.  SUMMARY  OF  RESULTS 


Careful  investigations  nave  been  made  of  tne  ratio  e/m  and 

o 

tne  results  are  in  good  agreement  witn  tne  value  1.77  x 10'  original- 
ly found  by  Kaufmann  for  catnode  rays.  The  following  are  some  of  the 
recent  determinations,  _e  being  expressed  in  electromagnetic  units. 

Slowly  moving  becquerel  rays,  oy  magnetic  ana  electro- 
static deflection: 

Kaufman  1.884x  107  (1906) 

Buchner  1.766  x 107  (1909) 

Neumann  1.765  x 107  (1915) 

Cathode  Rays: 

Bestelmeyer  1.73  x 107  (1907)  Magnetic  and  eiec.defl, 

Malassez  1.769  x 107  (1911)  n " " " 


between  electrod 

Catnode  Rays  from  glowing  oxides,  by  magnetic  deflection  and 
potential  difference  oetween  electrodes: 

Classen,  1.776  x 107  (1908) 

7 

Besrelmeyerl. 766  x 10  (1911) 

Photoelectric  effect  of  magnetic  deflection  ana  potential 
difference  between  tne  electrodes: 

Allusti  1.756  x 107  and  1.766  x 107  (1913) 

Zeeman  effect: 


Weiss  and  Colton 

1.767 

X 

107 

(1907) 

Stellenheimer 

1.  791 

X 

£V 

O 

i — i 

(1907) 

Omens  s 

1.771 

X 

107 

(1909) 

(13 


!i:w- 


. 


. 


32 


TABLE  OF  VALUES  OF  e/m 


e 


Source  of 
Ions 

Observer 

Date 

Method  of  Value 

Determination  of  e/m 

v • 10  “ 

Cat node 

ray  8 

J.  J. Thomson 

1897 

g 

Magnetic  and  7.7  x 10 
electrostat ic 
deflection 

2. 2-3. 6 

Catnode 

rays 

J.  J. Thomson 

1897 

Magnetic  de-  1.17  xlO7 
flection  and 
heating  ef- 
fect 

2* 4-3* 2 

Catnode 

rays 

Kaufrnann 

1897-8 

Magnetic  de-  1.86xl07 

flection  and 
potential  dif- 
ference 

Cathode 

rays 

Simon 

1899 

7 

Magnetic  de-  1.865  x10 
flection  and 
potential  dif- 
f er  enc  e 

Catnode 

rays 

Wie chert 

1899 

Magnetic  de-  1.01  x 107- 
f lection  and  1.55  x 107 
velocity  of 
ions 

Cathode 

rays 

Seitz 

1901 

Magnetic  and  6.45  x 10^ 
electrostat ic 
deflection 

7*  03 

Cathode 

rays 

Seitz 

1902 

Magnetic  and  1.87  x 107 
electrostatic 
deflection, 
heating  ef- 
fect amd  po- 
tential dif- 
ference 

5. 7-7. 5 

Cathode 

rays 

Starke 

1903 

Magnetic  and.  1.84  x 107 
electrostat ic 
deflection 

3.8-12 

Cathode 

rays 

Reiger 

1905 

Magnetic  de-  1.32  x 107 
flection  and 
potential  dif- 
ference 

Cathode 

rays 

Becker 

1905 

7 

Magnetic  de-  1.8  x 10 
flection  and 
retardation  in 
electric  field 

10 

. 


. 


33 


Source  of 

Observer 

Dat  e 

Metnod  of 
Determination 

Value  _g 

of  e/m  v • 10 

Lenard  rays 

Lenard 

1898 

Magnetic  and 
electrostat ic 
deflection 

6.39  x I06 

Lenard  rays 

Lenard 

1898 

Magnetic  de- 
flection and 
retardation  in 
electric  field 

6.8  x 106  3.4-10 

Ultra-violet 

light 

J. J. Thomson 

;899 

Retardation  of 
discharge  by 
magnetic  field 

7r6  x 106 

Ultra-violet 

light 

Lenard 

1900 

Magnetic  de- 
flection and 
potential  dif- 
ference 

1.15*  107 

Ultra-violet 

light 

Reiger 

1905 

Magnetic  de- 
flection and 
potential  dif- 
ference 

9.6  x 10®- 
1.3  x 107 

Incandescent 

metals 

J. J. Thomson 

1899 

Retardation  of 
discnarge  by 
magnetic  field 

8.7  x 106 

Incandescent 

oxides 

Owen 

1904 

Retardation  of 
discharge  by 
magnetic  field 

5.6  X 10® 

Incandescent 

oxiaes 

Wehnelt 

1904 

Magnetic  de- 
flection and 
potential  dif- 
ference 

1.4  x ll7 

Radium 

Becquer el 

1900 

Magnetic  and 

electrostatic 

deflection 

107  approx-  3 x 10^ 
imately 

Radium 

Kaufmann 

1901-3 

Magnetic  and 

electrostatic 

deflection 

1.77  x 107 
f or  small 
velocities 

Polonium 

Ewers 

1906 

Magnetic  and 

electrostatic 

deflection 

1.7  x 107 

« 


. 


. 


s 


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b4 


VI.  COwOLUSIOwS 

If  compared,  witn  the  charge  on  a univalent  ion  in  a liquid 
electrolyte  tne  cnarge  of  tne  negative  ion  obtained  in  nign  vacua 
will  be  found  to  be  tne  same,  Charge  is  not  effected  by  pressure  so 
tnere  is  a good  reason  to  believe  tnat  tne  cnarge  is  tne  same  a z all 
pressures. 

Tne  large  value  of  e/m  Obtained  for  negative  ion  is  due  to 
tne  smallness  of  m wnicn  is  less  tnan  tne  mass  of  an  atom  of  nydro- 
gen  in  tne  proportion  1:1830. 

Kaufman  investigated  tne  ratio  e/m  at  nigner  velocities 

approacning  to  tnat  of  light,  and  found  tnat  tne  value  of  e/m  dimin- 

7 

isnes  from  tne  small  velocity  value  to  l.ol  x 10  , wnen  the  velocity 
is  3.36  x lO1^  and  to  .63  x 10^  when  the  velocity  is  3.33  x 10^°. 

This  fact  has  an  important  bearing  on  electromagnetic  theory 
When  an  electric  charge  is  in  motion  tnere  is  a certain  amount  of 
electromagnetic  energy  resident  in  the  surrounding  field,  and  the 
charge  when  accelerated  exhibits  the  phenomena  of  inertia,  even  when 
supposed  to  devoid  of  ordinary  mass. 

When  the  velocity  approaches  that  of  lignt  the  mass  of  an 
electron  increases,  while  for  slow  speeds  the  electromagnetic  mass 
is  in  the  order  of  e3/a.  j is  the  charge  and  a is  the  radius  of  the 
electron. 

For  acceleration  in  the  direction  of  motion  tne  charge  be- 
haves as  though  it  had  a mass  ^(longitudinal  electromagnetic  mass). 
While  for  acceleration  at  right  angles  to  the  direction  of  motion  it 
appears  to  have  a different  mass  transverse  electromagnetic  mass). 

Abraham  and  Lorentz  in  their  theoretical  investigations 


. 


. 


. 


. 


35 


have  mentioned  that  the  longitudinal  mass  is  greater  tnan  the  trans- 
verse mass.  Abraham’s  theory  considers  the  electron  as  rigid,  and 
Lorentz’s  theory,  for  a special  reason,  considers  it  as  contracting 
in  the  direction  of  the  motion. 

Lorentz’s  theory  leads  to  the  following  formulae  for  m^ 
and  in  terms  of  the  velocity  v of  the  particle. 

ml  = U-vVc2)0^2 

= mQ/  ( 1- v2  / c3 ) 

both  masses  being  equal  to  m when  v is  small  compared  with  £ the  velo  - 
city  of  light. 

This  theory  is  justified  since  Kaufman’s  original  determin- 
ation of  the  transverse  electromagnetic  mass  and  the  recent  experi- 
ments of  Bucheret  with rays,  and  those  of  Hupka  on  fast  cathode 
rays,  are  in  agreement  with  it. 

All  this  supports  the  view  that  the  mass  of  an  electron  is 
entirely  electromagnetic. 

My  most  grateful  acknowledgments  are  due  to  Professor  A.P. 
Carman,  Head  of  the  Department,  ana  to  Professor  C.T.  Knipp.  The 
former  afforded  me  all  the  facilities  that  were  necessary  to  improve 
my  knowledge,  and  generously  helped  me  in  every  way  possible  in  my 
work.  I am  mucn  indebted  to  that  knowledge  and  information  which  is 
acquired  by  one  who  has  had  the  privilege  of  working  in  the  Labora- 
tory of  Physics  of  the  University  of  Illinois  under  Professor  C.T. 
Knipp  who  gave  invaluable  suggestions  and  also  made  a critical  re- 
vision of  the  manuscript  before  it  w'as  typewritten  in  the  final  form. 


. 


. 


. 


. 

. 

. . 


, ■■  ' . . . 


BIBLIOGRAPHY 


Crowther,  J.A.-  "Ions,  Electrons,  ana  Ionizing  Radiac ion, iyi9. 
Millikan,  R.A. - "The  Electron",  lyl7. 

Ramsay,  Sir  William  - "Elements  ana  Electrons",  1912. 

Thomson,  J.J.-  "Conduction  of  Electricity  tnrough  Gases",  1906; 

Philosophical  Magazine,  Vol.44,  p 293,(1897); 
Pmlosopnical  Magazine,  Vol.48,  p 547,  (1899). 
Townsend,  J.S.-  "Electricity  in  Gases",  1915. 

Schuster,  A. - Proc.  Royal  Society  of  London,  Vol.47,  p 045  (1890/. 


